Entrainment and detrainment are two fundamental processes in fluid mechanics that govern the mixing and movement of fluids within turbulent flows. The entrainment hypothesis, introduced by G.I. Taylor over 80 years ago, posits that the mean inflow velocity across the boundary of a turbulent flow is proportional to a characteristic velocity of the flow. This simple yet powerful model remains a cornerstone in environmental engineering and geophysical fluid dynamics, effectively describing phenomena such as convective clouds, volcanic plumes, oceanic overflows, and magma injections.

Entrainment primarily occurs through the engulfment of ambient fluid by large-scale eddies, which alters the density and dynamic properties of the turbulent flow. This process is evident in natural occurrences like chimney plumes widening as they rise, or volcanic ash clouds expanding horizontally. The entrainment velocity (We) can be expressed as We = EU, where U is a characteristic velocity scale, and E is the entrainment coefficient. The value of E is generally constant for plumes aligned with gravity but varies with the Richardson number (Ri) in buoyancy-driven flows like gravity currents, reflecting the stabilizing effect of buoyancy.

Detrainment, conversely, refers to the expulsion of fluid from turbulent regions back into the surrounding environment. While entrainment introduces external fluid into a turbulent system, detrainment governs the outflow, playing a crucial role in maintaining the mass and energy balance within the flow. Detrainment is influenced by factors such as flow stability, stratification, and the dynamics of internal wave breaking, especially in strongly stratified environments where interfacial perturbations are minimal.

The interaction between entrainment and detrainment is critical for understanding turbulent flow behavior. Entrainment drives the growth and mixing of turbulent regions, while detrainment regulates the dispersal and stabilization of the flow. For example, in gravity currents, entrainment enhances the mixing of dense fluids with lighter ambient water, whereas detrainment facilitates the release of mixed fluid, impacting the overall density and flow structure.

Both processes are essential in parameterizing turbulent mixing in numerical models, especially in general circulation models (GCMs) used for oceanography and atmospheric sciences. The entrainment coefficient's dependence on Ri and its modifications for different flow conditions highlight the complexity of accurately representing these dynamics in models.

In summary, while entrainment focuses on the inward flux of ambient fluid driven by turbulent eddies, detrainment manages the outward flux, ensuring the dynamic equilibrium of turbulent systems. Understanding their interplay is vital for predicting and modeling various geophysical and environmental fluid dynamics phenomena.

Mossa, M., De Serio, F. Rethinking the process of detrainment: jets in obstructed natural flows. Sci Rep 6, 39103 (2016). https://doi.org/10.1038/srep39103 investigate the phenomenon of detrainment in obstructed natural flows, a process traditionally associated with buoyancy-driven flows, such as plumes or density currents in stratified environments. However, the findings of this research reveal a critical innovative aspect: detrainment can also occur in momentum-driven turbulent jets released into non-stratified obstructed flows, such as vegetated environments. Theoretical and experimental analyses demonstrate that the presence of porous obstructions (e.g., vegetation canopies) inhibits the typical entrainment process—characteristic of free turbulent jets—while promoting fluid mass loss from the jet to the surrounding environment.

The main innovations include:

1. Redefinition of the conditions for detrainment: The process is not solely dependent on density gradients but can also be triggered by structural obstacles that alter turbulent dynamics.
2. Formulation of entrainment coefficient equations: These show negative values in the presence of obstructions, indicating a net release of fluid (detrainment) rather than assimilation.
3. Experimental validation: Laboratory data confirm the reduction of jet flow in obstructed environments, contrasting with the increased flow observed in unobstructed conditions.

This study broadens the understanding of mass transport and interactions between turbulent jets and obstructed ambient flows, with significant implications for aquatic ecosystem management, pollutant dispersion, and hydraulic engineering design.